t. j. peters kerner graphics topologically encoded animation (tea): history & future
Post on 21-Dec-2015
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Contemporary Computational Influences
• Edelsbrunner: geometry & topology
• Sethian: Marching methods, topology changes
• Blackmore: differential sweeps
• Carlsson, Zomordian : Algebraic
Little reuse or modification
“Plus, we love to blow things up.”
Digital Visual Effects (DVFX)
TEA: dimension-independent technology
• Provably correct temporal antialiasing
• Portability of animation to differing displays
• Efficient compression and decompression
Mappings and Equivalences
Knots and self-intersections
Piecewise Linear (PL) Approximation
My Scientific Emphasis
Moore Dissertation 2006
Efficient algorithm for ambient isotopic PL approximation for Bezier curves of degree 3.
Good Approximation!
Respects Embedding:
Curvature (local) &Separation (global)
Error bounds!! =>Nbhd_2 about curve.
But recognizing unknot in NP (Hass, L, P, 1998)!!
Temporal Antialiasing Comparison
• Time to market.
• Produce traditionally.
• Produce with TEA technology.
Compression: TEA File (<1KB vs 1.7 Megs)
Bezier degree = 3, with Control points 0.0 0.0 0.0 4.293 4.441 0.0 8.777 5.123 1.234 12.5 0.0 0.0
Perturbation vectors; constraint on each vector 1 24.1 0.0 0.0 ; 26.4 1 -12.5 0.0 5.0 ; 18.1 2 -2.1 -2.4 -3.1 ; 9.0 1 -11.6 0.0 -1.9 ; 14.0
Conclusions
• Time can be modeled continuously while frames remain discrete.
• Difference between
– Perturb then approximate versus
– Approximate then perturb.
Quotes & Interpretation
• “You can’t rush art.”, Woody, Toy Story 2
• “Time is money”.
• Correct math for the most money.
Overview References• Modeling Time and Topology for Animation
and Visualization, [JMMPR], pre-print
• Computation Topology Workshop, Summer Topology Conference, July 14, ‘05, Special Issue of Applied General Topology, 2007
• Open Problems in Topology II, 2007
• NSF, Emerging Trends in Computational Topology, 1999, xxx.lanl.gov/abs/cs/9909001
Acknowledgements: NSF
• SBIR: TEA, IIP -0810023 .
• SGER: Computational Topology for Surface Reconstruction, CCR - 0226504.
• Computational Topology for Surface Approximation, FMM - 0429477.
• Investigator’s responsibility, not NSF.